Dissertation_XiaoquanGao.pdf

Public sector services often face challenges in allocating limited resources effectively. Despite their fundamental importance to societal welfare, these systems often operate without sufficient analytical support, and their decision-making processes remain understudied in academic literature. While data-driven analytical approaches offer promising solutions for addressing complex tradeoffs and resource constraints, the unique characteristics of public systems create significant challenges for modeling and developing efficient solutions. This dissertation addresses these challenges by applying stochastic models to enhance decision-making in two critical areas: emergency medical services in healthcare and jail diversion in the criminal justice system.The first part focuses on integrating drones into emergency medical services to shorten response times and improve patient outcomes. We develop a Markov Decision Process (MDP) model to address the coordination between aerial and ground vehicles, accounting for uncertain travel times and bystander availability. To solve this complex problem, we develop a tractable approximate policy iteration algorithm that approximates value function through neural networks, with basis functions tailored to the spatial and temporal characteristics of the EMS system. Case studies using historical data from Indiana provide valuable insights for managing real-time EMS logistics. Our results show that drone augmentation can reduce response times by over 30% compared to traditional ambulances. This research provides practical guidelines for implementing drone-assisted emergency medical services while contributing to the literature on hybrid delivery systems.The second part develops data-driven analytical tools to improve placement decisions in jail diversion programs, balancing public safety and individual rehabilitation. Community corrections programs offer promising alternatives to incarceration but face their own resource constraints. We develop an MDP model that captures the complex tradeoffs between individual recidivism risks and the impacts of overcrowding. Our model extends beyond traditional queueing problems by incorporating criminal justice-specific features, including deterministic service times and convex occupancy-dependent costs. To overcome the theoretical challenges, we develop a novel unified approach that combines system coupling with policy deviation bounds to analyze value functions, ultimately establishing the superconvexity. This theoretical foundation enables us to develop an efficient algorithm based on time-scale separation, providing practical tools for optimizing diversion decisions. Case study based on real data from our community partner shows our approach can reduce recidivism rates by 28% compared to current practices. Beyond academic impact, this research has been used by community partners to secure program funding for future staffing.